Given:
∠C = 45°
AB = 12√3
For us to be able to get the measure of side BC, we will be using the Tangent Function:
[tex]\text{ Tangent }\Theta\text{ = }\frac{\text{ Opposite }}{\text{ Adjacent}}[/tex]
Where,
Θ = ∠C = 45°
Opposite = AB = 12√3
Adjacent = BC
We get,
[tex]\text{ Tangent \lparen45}^{\circ})\text{ = }\frac{\text{ 12}\sqrt{3\text{ }}}{\text{ BC}}[/tex][tex]\text{ BC = }\frac{\text{ 12}\sqrt{3\text{ }}}{\text{ Tangent \lparen45}^{\circ})}[/tex][tex]\text{ BC= }\frac{\text{ 12}\sqrt{3}}{\text{ 1}}\text{ = 12}\sqrt{3}[/tex]
Therefore, the answer of BC is 12√3, the triangle is an isosceles triangle.
The answer is CHOICE C.
